Liquid to vapor-liquid, liquid-liquid to vapor-liquid-liquid, and liquid to liquid-liquid transition pressures of (alpha-olefin + n-hexane + LLDPE) systems were measured using a newly constructed and verified synthetic-visual high-pressure cell and metallocene linear low-density polyethylene (LLDPE: (M) over bar (w) = 199 kg.mol(-1), (M) over bar (w)/(M) over bar (n) = 2.62, 2.56 mol % 1-hexene). New phase behavior data are reported for a quasibinary (n-hexane + LLDPE) system at polymer mass percentages of w(p) = (0.5-5) wt % and quasiternary (alpha-olefin + n-hexane + LLDPE) systems for w(p) = 3 wt % and polymer-free alpha-olefin mass percentages of up to 3 wt % ethylene, 20 wt % 1-butene, 100 wt % 1-hexene, 30 wt % 1-octene, and 30 wt % 1-decene. The reported data span temperatures of T = (380-470) K and pressures of P = (0.5-13) MPa. They show that (i) transition temperatures and pressures change linearly with alpha-olefin mass fraction in the solvent; (ii) the C-2 to C-6 alpha-olefins decrease, and the C-8 to C-10 alpha-olefins increase the transition temperatures; and (iii) ethylene has a significant antisolvency effect. The measured data are correlated and predicted successfully with the modified Sanchez-Lacombe equation of state.